In this section, we compare the performance of discrete and integrated processors shown in Figs. 1(b) and (c), respectively. Although the size, weight, and power consumption (SWaP) of integrated processors are greatly reduced compared with the discrete processors, the state-of-the-art integrated processors suffer from limited tap numbers due to the restrictions imposed by the integrated components. Currently, integrated processors with only 8 [42] and 12 taps [43] have been demonstrated, whereas discrete processors have been implemented with up to 80 taps [1, 44]. The difference in the tap numbers results in a difference in the processing accuracy [44]. In addition, the imperfect response of experimental components also induces processing errors. These mainly include noise of microcombs, chirp of the EOM, errors in the delay element, and errors of the spectral shaping module [44].
Table Ⅰ summarizes parameters of the components in the three processors that we investigate, including a discrete processor (Processor 1) and two integrated processors (Processors 2 and 3). There are two integrated processors: one with the same tap number as that in Ref. [42] and the other with an increased tap number to demonstrate the potential for improvement. To characterize the errors induced by imperfect experimental components, optical signal-to-noise ratios (OSNRs), chirp parameters (α), error of the delay element (tv), and random tap coefficient errors (RTCEs) are introduced. These parameters are all set based on the real processors in Refs. [43–47]. For comparison, we assume that the three processors employ the same microcomb with a comb spacing of 0.4 nm (~ 50 GHz). We also assume that the time delay between adjacent taps in Eq. (3) is ∆T = 33.4 ps to ensure the same operation bandwidth.
TABLE Ⅰ. COMPARISON OF COMPONENTS’ PARAMETERS IN DISCRETE AND INTEGRATED PROCESSORS
Discrete
processor
|
No.
|
Tap No.
|
OSNR of microcombs
|
Chirp parameter of the EOM
|
Errors of the delay element
|
RTCE of the spectral shaping module
|
1
|
M = 80 [44]
|
OSNR : 20 dB [44]
|
α : 0.1 [47]
|
tv : 4% [44]
|
RTCE : 5% [44]
|
Integrated
processors
|
No.
|
Tap No.
|
OSNR of microcombs
|
Chirp parameter of the EOM
|
Error of the delay element
|
RTCE of the spectral shaping module
|
2
|
M = 8 [42]
|
OSNR : 20 dB [44]
|
α : 0.8 [45]
|
tv : 3% [43]
|
RTCE : 9% [46]
|
No.
|
Tap No.
|
OSNR of microcombs
|
Chirp parameter of the EOM
|
Error of the delay element
|
RTCE of the spectral shaping module
|
3
|
M = 20
|
OSNR : 20 dB [44]
|
α : 0.8 [45]
|
tv : 3% [43]
|
RTCE : 9% [46]
|
Compared with discrete EOM, the integrated EOM has a relatively high chirp parameter in Table I, mainly because achieving an accurate bias point and precise electrode placement is more challenging for integrated devices [47]. The lower accuracy for the delay element in the discrete processor is mainly caused by the high-order dispersion of the dispersive medium (e.g., optical fibre), which results in non-uniform time delays between adjacent wavelength channels [44]. In contrast, in integrated processors time delay is introduced by integrated optical delay lines (e.g., Si spiral waveguides), which exhibit a higher accuracy owing to the precise control over the amount of delay achieved by designing specific length and refractive index profile [48]. The accuracy differences between the integrated and discrete spectral shaping modules are more noticeable. Although the integrated spectral shaping modules have much lower tap numbers, they have lower spectral shaping accuracy compared to their discrete counterparts. This is due to the fact that commercial discrete waveshapers based on mature liquid crystal on silicon (LCoS) technology offer much better accuracy for amplitude and phase control, as well as inter-channel synchronization [49].
In our following analysis, three typical signal processing functions including first-order differentiation (DIF), integration (INT), and Hilbert transform (HT) are taken as examples to compare the accuracy of discrete and integrated processors. The tap numbers required to achieve these processing functions are designed based on our previous work in Refs. [1]. To quantify the comparison of processing accuracy, the root mean square error (RMSE) is introduced to compare the deviation between the processors’ outputs and the ideal results, which is expressed as
$$\text{RMSE = }\sqrt{\underset{\text{i}\text{=1}}{\text{∑}^{\text{k}}}\frac{\text{(}{\text{Y}}_{\text{i}} \text{–}\text{ }{\text{y}}_{\text{i}}\text{)}\text{2}}{\text{k}}}$$
4
where k is the number of sampled points, Y1, Y2, …, Yn are the values of the ideal result, and y1, y2, …, yn are the values of the output of the processors.
Figures 2(a) – (c) show the outputs of Processors 1–3 in Table I that perform DIF, INT, and HT, respectively. The input RF signal is a Gaussian pulse with a full-width-at-half-maximum (FWHM) of ~ 0.17 ns. Here we show the processors’ outputs with errors induced by (1) only limited tap numbers and (2) both limited tap numbers and experimental errors. The ideal processing results are also shown for comparison. Deviations between the processors’ outputs and the ideal results are observed for all three functions, and the deviations become more significant when taking into account the experimental errors.
Figure 3 compares RMSEs of the processors in Fig. 2. The higher processing accuracy of the discrete processor, compared to the integrated processors, is reflected by the lower RMSEs of Processor 1 for all three processing functions. In addition, the RMSEs of Processor 3 are lower compared to Processor 2, which indicates a higher processing accuracy achieved by increasing the tap number. According to the results in Fig. 3, the primary factor that contributes to the degradation of accuracy for integrated processors is the limited tap number. Whereas for discrete processors with a sufficiently large tap number, the processing inaccuracy is mainly induced by the imperfect response of experimental components. We also note that the differences in RMSEs among Processors 1–3 are more prominent for the INT than the other two processing functions, indicating a higher requirement for a greater number of taps to improve the processing accuracy of INT. In addition, experimental errors have a substantial impact on the RMSEs of DIF, whereas their impact on HT is very small.